This sense of lid is still common today in Amateur ("Ham") Radio (in the United States, at least), usually as "they're a lid", meaning "they're being a rude or unobservant person." It doesn't refer to new operators, usually, as much as someone who is willfully ignoring convention.

I can't really see how this originates from any meaning of lid; the most plausible origin to me seems the phrase "put a lid on", because as an operator, a lid "silences" others or "puts a crimp" in their operating.

"...taking care not to play the lid—"
"Lid?" questioned Soc.
"A lid is a radio operator who is either fresh from school or hasn't taken the trouble to learn to use his head and his fist at the same time."

It occurred to me that early use of "lid" isn't really about personal character - it seems to be saying someone is a newbie or has bad operating technique. The way I hear it used today is more about being a jerk (for example, a fellow ham remarks, "What a lid!" in regard to a guy who complains it's difficult to copy one of our female operators' voices compared to a male one). This mention from early 1900s, though it seems to paint all hams with the same brush, does seem to show a bit of that "unsophisticated/ignorant jerk" connotation.
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aedia λJun 28 '11 at 20:41

1912 antedating

And if some "Ham" who sounds insane,
Should move me to say things profane
O stay my hand upon the key
And may I not get "H" for "P."

May I refrain to ope my door
And kick through it some tedious bore.
Who brings to me his half-wit kid
To be transformed into a lid.

A slight variation appears in Telephony of 1913, which gives us the full text and quotes around jargon terms, and a source:

Help ! Help !

Poetry will out, sometimes in the most unexpected places and occasionally from unusual sources, says the Los Angeles (Cal.) Times. One of the latest devotees of the muse and one who has been creating considerable comment around the Alexandria is little Miss Vivian Ewing, Postal Telegraph operator in the hotel. After months of viccisitudes and troubles caused principally by the patrons of the little station in the marble corridor, Miss Ewing evolved the following prayer to assist her through her hours of toil:

Help me this day, O, Lord, to be
Kind and gentle with my key.
Help me earn my wage this day
And tempt me not to ask more pay;
And if some man who sounds insane
Should move me to hot things profane,
O stay my hand upon the key
And may I not make "H" for "P".

May I refrain to open my door
And kick through it a weary bore
Who brings to me his darling “kid”
To be transformed into a “lid”.
And may I gently treat the cranks
Who, after spoiling twenty blanks,
Fold up a lot of callow slush
And sternly bid me, “send it rush".

And when the clock points five to eight,
O, help me then to calmly wait
While some proud dad leans on the booth
And wires baby has a tooth.
In short, pray make me what I ain't,
An understudy of a saint,
That I may hold this job of mine
Till time gives me the "30" sign.

C. A. Shock, of Sherman, Texas, sent this to TELEPHONY with the suggestion that variations might be rung on it to make it apply to the telephone operator. So, “potes," sharpen pencils and have at it!

These are from snippets, so the years could be wrong, but it appears to have been reprinted in other magazines published between 1912-1914.

Lid operator

A lid operator, or lid, was originally a novice operator, rather than any poor operator.

The "lid" operator can be told very quickly when he makes a mistake. He does not use a definite "error" signal but usually betrays himself by sending a string of dots. The good operator sends "I ?" after his mistakes and starts sending again with ...

When you have traffic and want to get it off, DO NOT give it to a "lid" operator. If you do, the chances are that It will die right there. Many times I have become QSO with several stations in one direction, with the intention of QSRlng, only to find ...

We plead guilty to "getting quite a kick out of" operating our radio phone sets. The idea seems to prevail that no one except a "ham", a "lid" or a rank beginner even fools with phone. Unfortunately this is true to some extent but there are old ...

And:

... I flatter myself that I have become more than just a lid operator. I hold a commercial license, am an ORS and have made a fair showing in traffic, and to you, OM, I owe a great part of my success. You were my first schedule and I have tried to ...

And:

... gave several humorous anecdotes of his first trip as a "lid" commercial operator on the Great Lakes.

Can it be a New Year's resolution, and that he is starting at the bottom like an inexperienced "lid"? Two nasty accidents occurred in "Mu" since the advent of the New Year. Andy and Archie fell off the booze-wagon. Nothing serious happened ...

However, Popular Science (1933) quoted in the question is all about trade jargon, and includes an English translation of "Telegrapher's Lingo". The full description is of a novice, but specifically translates lid as poor, showing the meaning is changing:

He uses a bug, but it runs away with him. As a sender he's a lid.

...

Translated, this queer language means:

He uses a semi-automatic key, but keeps it adjusted at a speed greater than that at which he can manipulate it properly. As a sender of messages he is poor.

It goes on to praise him for being able to receive at the fastest speeds and for never interrupting. (It also explains what "30" means, as mentioned in the 1919 poem.)

Sitting on the lid

This may be unrelated, but I'll include it on the off chance. The Railroad Telegrapher included reports of union members' work situation ("In 1920, there were 78,134 telegraphers on all railroads represented by The Order of Railroad Telegraphers. Membership in the union had peaked."). Some of these would include the phrase "is sitting on the lid". Here are some examples.

From the preceding 1913 Telephony:

I. S. Johnson and Leo Smiddy are working extra there, while Bro. Bob Fountaine sits on the lid.

Bros. Packard, Wilson and Nickel sat on the lid while Bro. Hook attended the TOI'0.'ll0 [?] convention and took a trip through the East. He was relieved by Bro. _l. L. Druley, from the \'abash [?].

And here:

... rear brakeman on the division correspondent's motorcycle for several miles. I introduced him to the high and low crossings at a speed of 30 miles per, when we stopped he had both legs wrapped around the gas tank, and was settin' on his lid.

And here:

Mr. John Dalzell, Chairman of the Rules Committee, sat stubbornly "on the lid" and refused to budge. He believes that free trade in labor is the safest bulwark of tariff protection for employers.

Two operators taken off at Merino, making it
a one-man station, with Bro. Johnson on the lid.
Bro. Doherty to second Brighton, bumping Bro.
Baker to second Carr, vice Bro. Seeley bumping
Bro. Rotenbaum; Dent nights to the extra list.

I'm not entirely clear what this sitting on the lid refers to, but for the work reports, I get the impression it's similar to sitting on the bench, being held as reserve.

One of these is not a work report but a political report: "Mr. John Dalzell, Chairman of the Rules Committee, sat stubbornly "on the lid" and refused to budge." This has a political meaning, according to A Desk-Book of Errors in English (1906, 1920) by Frank Horace Vizetelly:

lid: A slang term for cover, hat, etc., used especially in the phrases keeping the lid down, sitting on the lid, political colloquialisms for closing up places of business, as pool-rooms, saloons, etc., or keeping a political situation in control.

This fits for the stubborn chairman of the rules committee, and speculating, perhaps this "keeping control" sense was applied to reserve workers patiently waiting their turn. Or perhaps the union work reports are telling us those workers were taking care of union business and keeping their local situation in control.

In any case, the political phrase "sitting on the lid" originated or was at least popularised by President Theodore Roosevelt when describing Secretary of War, William Howard Taft:

Taft as Secretary of War became the administration's "trouble shooter" at home and abroad. During the years between 1904 and 1908 Taft had direct charge of the construction of the Panama Canal. Roosevelt considered Taft one of his most valuable assets, so able was Taft that Roosevelt felt free to leave the capital whenever he wished, because he had "left Taft sitting on the lid." As Roosevelt's personal emissary Taft was sent on many diplomatic assignments.

This phrase went around the country at the time, and the fact that Mr. Taft's physical weight was such that we all had a feeling that if he were sitting on the lid, the lid must be geld down pretty firmly, undoubtedly had much to do with the success of the great phrase-maker's remark at that time.

More speculation: "sitting on the lid" was a metaphor for "sitting on a hat" meaning "keeping control" and the meaning passed to "sitting as a reserve on the bench". Operators sitting in reserve are often novice operators, or "lid operators". A lid operator was then originally a novice worker, and as novice workers would make more mistakes, the meaning then changed to refer to any poor operator.

Thank you so much for all the research! It didn't even occur to me that QST might be in Google Books. It's fascinating to see the evidence that "lid" meant "newbie operator" almost a hundred years ago.
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aedia λApr 5 '13 at 20:13

The truth is that nobody knows. It is an inherited title from the land-line (wired) Morse telegraphy days; that much is certain. But why "lid"?

I find the tobacco lid explanation unconvincing. The need to bring the annunciator's click frequency down using a mechanical resonator may indicate aged or damaged hearing, but it doesn't even imply incompetence on the operator's part.

The most convincing explanation I've heard is that a sender with poor rhythm sending "dd" (a common double letter, and the commonest with possible ambiguity) would send something that sounded like dah...dit-dit...dah-dit-dit ("l-i-d") rather than dah-dit-dit...dah-dit-dit ("d-d"). But that's just conjecture with a bit of history behind it, just like the Prince Albert tobacco theory.

It does seem plausible that lid could be mistaken for dd and vice-versa in American Morse: L in this alphabet is a double length 'daaah' that doesn't exist in the International Morse used today. Now at least I don't have to worry whether you said daaah dit dit or dah dit dit :)
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aedia λJun 28 '11 at 0:25

It could boil down to a particular case. It could be one operator was known as a jerk, and also well known for using the tobacco lid trick. The person known as "lid" could have become an archetype for idiocy, just like Einstein is an archetype for genius. Again, this is conjecture without some record of such a person.